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<table width="100%"><tr><td>trun(gamlss.tr)</td><td align="right">R Documentation</td></tr></table><object type="application/x-oleobject" classid="clsid:1e2a7bd0-dab9-11d0-b93a-00c04fc99f9e">
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<h2>Fits a Truncate Distribution from a gamlss.family</h2>


<h3>Description</h3>

<p>
This function can be used to fit truncated distributions. It takes as an argument an existing GAMLSS family distribution and 
a parameter vector,  of the type c(left.value, right.value), and  generates a <code><a onclick="findlink('gamlss', 'gamlss.family.html')" style="text-decoration: underline; color: blue; cursor: hand">gamlss.family</a></code> object which then can be used to fit 
a truncated distribution.
</p>


<h3>Usage</h3>

<pre>
trun(par = c(0), family = "NO",  type = c("left", "right", "both"), name = "tr", 
        local = TRUE, delta=NULL, ...)
</pre>


<h3>Arguments</h3>

<table summary="R argblock">
<tr valign="top"><td><code>par</code></td>
<td>
a scalar for left and right truncation or a vector of the type c(left.value, right.value) for interval truncation</td></tr>
<tr valign="top"><td><code>family</code></td>
<td>
an existing <code><a onclick="findlink('gamlss', 'gamlss.family.html')" style="text-decoration: underline; color: blue; cursor: hand">gamlss.family</a></code> distribution</td></tr>
<tr valign="top"><td><code>type</code></td>
<td>
what type of truncation is required, <code>left</code>, <code>right</code> or <code>both</code>. If <code>both</code> the <code>par</code> should be a vector of length two. (the default is left truncation)</td></tr>
<tr valign="top"><td><code>name</code></td>
<td>
a character string to be added to name of the created object i.e. with <code>family=TF</code> and <code>name=trZero</code> the <code><a onclick="findlink('gamlss', 'gamlss.family.html')" style="text-decoration: underline; color: blue; cursor: hand">gamlss.family</a></code> object will be called <code>TFtrZero</code></td></tr>
<tr valign="top"><td><code>local</code></td>
<td>
if TRUE the function will try to find the environment of <code>gamlss</code> to generate the <code>d</code> and <code>p</code> functions required for the fitting, if FALSE the functions will be generated in the global environment</td></tr>
<tr valign="top"><td><code>delta</code></td>
<td>
the delta increment used in the numerical derivatives</td></tr>
<tr valign="top"><td><code>...</code></td>
<td>
for extra arguments </td></tr>
</table>

<h3>Details</h3>

<p>
This function is created to help the user to fit a truncated form of existing <code>gamlss</code> distribution.
It does this by taking an existing <code><a onclick="findlink('gamlss', 'gamlss.family.html')" style="text-decoration: underline; color: blue; cursor: hand">gamlss.family</a></code> and changing some of the components of the distribution to help the fitting process. 
It particular it i) creates a pdf (<code>d</code>) and a cdf (<code>p</code>) function within <code>gamlss</code>, 
ii) changes  the global deviance function <code>G.dev.incr</code>, the first derivative functions (see note below) and the quantile residual function.
</p>


<h3>Value</h3>

<p>
It returns a <code><a onclick="findlink('gamlss', 'gamlss.family.html')" style="text-decoration: underline; color: blue; cursor: hand">gamlss.family</a></code> object which has all the components needed for fitting a distribution in <code>gamlss</code>.</p>

<h3>Note</h3>

<p>
This function is experimental and could be changed. The function <code>trun</code>  changes 
the first derivatives of the original gamlss family <code>d</code> function to numerical derivatives 
for the new truncated <code>d</code> function. The default increment <code>delta</code>,
for this numerical derivatives function, is <code>eps * pmax(abs(x), 1)</code> where 
<code>eps&lt;-sqrt(.Machine$double.eps)</code>.  The default <code>delta</code> could be inappropriate 
for specific applications and can be overwritten by using the argument <code>delta</code>.
</p>


<h3>Author(s)</h3>

<p>
Mikis Stasinopoulos <a href="mailto:d.stasinopoulos@londonmet.ac.uk">d.stasinopoulos@londonmet.ac.uk</a> and Bob Rigby <a href="mailto:r.rigby@londonmet.ac.uk">r.rigby@londonmet.ac.uk</a>
</p>


<h3>References</h3>

<p>
Rigby, R. A. and  Stasinopoulos D. M. (2005). Generalized additive models for location, scale and shape,(with discussion), 
<EM>Appl. Statist.</EM>, <B>54</B>, part 3, pp 507-554.
</p>
<p>
Stasinopoulos D. M., Rigby R.A. and Akantziliotou C. (2003) Instructions on how to use the GAMLSS package in R.
Accompanying documentation in the current GAMLSS  help files, (see also  <a href="http://www.gamlss.com/">http://www.gamlss.com/</a>).
</p>


<h3>See Also</h3>

<p>
<code><a href="trun.d.html">trun.d</a></code>, <code><a href="trun.p.html">trun.p</a></code>, <code><a href="trun.q.html">trun.q</a></code>, <code><a href="trun.r.html">trun.r</a></code>,  <code><a href="gen.trun.html">gen.trun</a></code>
</p>


<h3>Examples</h3>

<pre>
# generate a left truncated zero t family
gen.trun(0,family="TF")
# take a random sample of 1000 observations
sam&lt;-rTFtr(1000,mu=10,sigma=5, nu=5 )
hist(sam)
# fit the distribution to the data
mod1&lt;-gamlss(sam~1, family=trun(0,TF))
mod1
# now create a gamlss.family object before the fitting 
Ttruc.Zero&lt;- trun(par=0,family=TF, local=FALSE)
mod2&lt;-gamlss(sam~1, family=Ttruc.Zero)
# now check the sensitivity of delta 
Ttruc.Zero&lt;- trun(par=0,family=TF, local=FALSE, delta=c(0.01,0.01, 0.01))
mod3&lt;-gamlss(sam~1, family=Ttruc.Zero)
</pre>

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